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stira [4]
3 years ago
8

Is the system of equations is consistent, consistent and coincident, or inconsistent?

Mathematics
2 answers:
-Dominant- [34]3 years ago
8 0

Answer:

The given system of equations is inconsistent.

Step-by-step explanation:

We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.

y=-3x+12...(1)        

y=-6x+2...(2)

Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.

Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.

Now let us check slope of given lines.

Upon dividing equation (2) by 2 we will get,

y=-3x+1...(2)

We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.

Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.

Tems11 [23]3 years ago
4 0
The slope of (y=-3x+12) is -3 while the slope of (y=-6x+2) is -6. Therefore, it's Inconsistent. 
Coincident is one line on the graph
Consistent is two parallel lines

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Graphing polynomial functions?
Leni [432]

NOTES:

Degree: the largest exponent in the polynomial

End Behavior:

  • Coefficient is POSITIVE, then right side goes to POSITIVE infinity
  • Coefficient is NEGATIVE, then right side goes to NEGATIVE infinity
  • Degree is EVEN, then left side is SAME direction as right side
  • Degree is ODD, then left side is OPPOSITE direction as right side

Multiplicity (M): the exponent of the zero. <em>e.g. (x - 3)²  has a multiplicity of 2</em>

Relative max/min: the y-value of the vertices.  

  1. Find the axis of symmetry <em>(the midpoint of two neighboring zeros)</em>
  2. Plug the x-value from 1 (above) into the given equation to find the y-value. <em>(which is the max/min)</em>
  3. Repeat 1 and 2 (above) for each pair of neighboring zeros.

Rate of Change: slope between the two given points.

********************************************************************************************

1. f(x) = (x-1)²(x + 6)

a) Degree = 3

b) end behavior:

  • Coefficient is positive so right side goes to positive infinity
  • Degree is odd so left side goes to negative infinity

c) (x - 1)²(x + 6) = 0

   x - 1 = 0                     x + 6 = 0

       x = 1 (M=2)                   x = -6 (M=1)

d) The midpoint between 1 and -6 is -3.5, so axis of symmetry is at x = -3.5

y = (-3.5 - 1)²(-3.5 + 6)

  =  (-4.5)²(2.5)

  = 50.625

50.625 is the relative max

e) see attachment #1

f) The interval at which the graph increases is: (-∞, -3.5)U(1, ∞)

g) The interval at which the graph decreases is: (-3.5, 1)

h) f(-1) = (-1 - 1)²(-1 + 6)

          = (-2)²(5)

          = 20

    f(0) = (0 - 1)²(0 + 6)

          = (-1)²(6)

          = 6

Find the slope between (-1, 20) and (0, 6)

m = \frac{20-6}{-1-0}

   = \frac{14}{-1}

   = -14

********************************************************************************************

2.    y = x³+3x²-10x

         = x(x² + 3x - 10)      

         = x(x + 5)(x - 2)

a) Degree = 3

b) end behavior:

   Coefficient is positive so right side goes to positive infinity

   Degree is odd so left side goes to negative infinity

c) x(x + 5)(x - 2) = 0

   x = 0                     x + 5 = 0                     x - 2 = 0

   x = 0 (M=1)                   x = -5 (M=1)                x = 2 (M=1)

d) The midpoint between -5 and 0 is -2.5, so axis of symmetry is at x = -2.5

y = -2.5(-2.5 + 5)(-2.5 - 2)

  =  -2.5(2.5)(-4.5)

  = 28.125

28.125 is the relative max

The midpoint between 0 and 2 is 1, so axis of symmetry is at x = 1

y = 1(1 + 5)(1 - 2)

  =  1(6)(-1)

  = -6

-6 is the relative min

e) see attachment #2

f) The interval at which the graph increases is: (-∞, -2.5)U(1, ∞)

g) The interval at which the graph decreases is: (-2.5, 1)

h) f(-1) = -1(-1 + 5)(-1 - 2)

********************************************************************************************

3. y = -x(x + 2)(x - 7)(x - 3)

a) Degree = 4

b) end behavior:

   Coefficient is negative so right side goes to negative infinity

   Degree is even so left side goes to negative infinity

c)  -x(x + 2)(x - 7)(x - 3) = 0

  -x = 0                     x + 2 = 0                     x - 7 = 0             x - 3 = 0

   x = 0 (M=1)                 x = -2 (M=1)                x = 7 (M=1)          x = 3 (M=1)

d) The midpoint between -2 and 0 is -1, so axis of symmetry is at x = -1

y = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

  =  1(1)(-8)(-4)

  = 32

32 is a relative max

The midpoint between 0 and 3 is 1.5, so axis of symmetry is at x = 1.5

y = -(1.5)(1.5 + 2)(1.5 - 7)(1.5 - 3)

  =  -1.5(3.5)(-5.5)(-1.5)

  = -43.3125

-43.3125 is the relative min

The midpoint between 3 and 7 is 5, so axis of symmetry is at x = 5

y = -(5)(5 + 2)(5 - 7)(5 - 3)

  =  -5(7)(-2)(2)

  = 140

140 is the relative max

e) see attachment #3

f) The interval at which the graph increases is: (-∞, -1)U(1.5, 5)

g) The interval at which the graph decreases is: (-1, 1.5)U(5, ∞)

h) f(-1) = -(-1)(-1 + 2)(-1 - 7)(-1 - 3)

          = 1(1)(-8)(-4)

          = 32

    f(0) = -(0)(0 + 2)(0 - 7)(0 - 3)

          = 0

Find the slope between (-1, 32) and (0, 0)

m = \frac{32-0}{-1-0}

   = \frac{32}{-1}

   = -32



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balu736 [363]

Hello there!

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Jennifer stands 80 ft above sea level at the top of a lighthouse. she sees a boat sailing 400 ft from the lighthouse.what is the
satela [25.4K]

<span>Let </span>

<span>X=  the altitude of the lighthouse above sea level= 80 ft</span>

 A = the angle of depression 

Y= the distance of the boat from the lighthouse= 400 ft

 tan A=X/Y------------------ > 80/400=0.2

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Step-by-step explanation:

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